Distinguishing the General from the Generic / Lectures / Projective Theory of Technology / Thinking as an Algebraic Mechanist

Symbolic Solids, or: exploring Architecture’s Inverse // Architecture beyond Design

This is the documentation of my talk at The Building conference Columbia University GSAPP, organized by Jose Araguez with Aaron White.

The Building

15 November 2014, 9:30am to 5:30pm, Wood Auditorium, Columbia University GSAPP

Ever since the theoretical turn of the 1960s, right through to the present, the status of the architectural object in the sphere of history, theory and criticism keeps taking on more and more forms. Whether as the reification of power structures, as a facilitator of participatory processes, as the locus of phenomenological content, as the hypostatization of terms pertaining to other systems of thought, as a vehicle to reflect upon unmediated practices, as a catalyst to investigate the psychology of perception, as amenable to mirror processes in the natural world—its increasing epistemological diversification is an index for the growing sophistication of our field. Within this tendency, however, the object emerges more often as a medium through which to tap into another domain—if not as altogether absent—than it does as the ultimate realm of research in its own right.

This event suggests that discussions taking the object as their primary concern can today extend the bounds of possibility for the production of discursive knowledge in a substantial fashion. In order to do so, it invokes the architectural object par excellence—the building. A number of historians, theorists, architects and PhD candidates, from both Europe and the US, have been asked to choose a building, built or designed within the last 25 years, which they can show embodies a historically substantial contribution in terms of a particular design aspect or a concept relevant to the reading of buildings in general. In addition, they have been invited to speculate on the possibility for such a design technique or concept to become the seed of a metadisciplinary theoretical framework. The first installment of this event took place at the Architectural Association on June 2, 2014.

With Stan Allen, Jose Aragüez, Vera Bühlmann, Marta Caldeira, Juan Antonio Cortés, Marc Frochaux, Gabriela García de Cortázar, Francisco González de Canales, Costandis Kizis, Sylvia Lavin, Mary McLeod, Michael Meredith, Joan Ockman, Jorge Otero-Pailos, Sophia Psarra, Amanda Reeser Lawrence, Etien Santiago, Alexandra Vougia, Enrique Walker, Aaron White, Michael Young and Alejandro Zaera-Polo.


The work I chose was by Michael Hansmeyer. Here is an abstract and outline of the angle I took in discussing his work.

In his more recent work (Platonic Solids 2009; Subdivided Columns 2010/11; Digital Grotesque 2013 [together with Benjamin Dillenburger]), Michael Hansmeyer’s experiments in computational architecture manifest a powerful new vector of interest in digital architecture and culture: from analytic and calculus-based form to the algebraic character of computation more comprehensively. The fascination pertaining to ‘the object’ in Hansmeyer’s work regards an active force ‚the object‘ acquires through the very process of being computed. His experiments pursue what in modern registers must appear as a contradiction in terms: objectivity and indeterminateness need no longer count as mutually exclusive characteristics.

I will accentuate an interesting turn for critique in this curiosity: the classic opposition between, on the one hand, a strictly materialist interest in forces, and, on the other hand, an idealist interest in subjectivity, is being rendered here as something that fits neither one of these polarities – I will suggest to speak, instead, of it as the symbolico-physical solidity of crystallization processes. My position will be that we can read Hansmeyer’s work as attempts to ‚alphabetize‘ computationally architectures typologies. A key concern thereby is how this conservative gesture relates to the pragmatic goal of architecture: namely to ‚modernize’.

A computational approach enables architecture to be embedded with an extraordinary degree of information. 

(Michael Hansmeyer: http://www.michaelhansmeyer.com)

Materialist informatics

I will try to foreground a materialist view in which the object is endowed with forces, yet not in a manner that would harvest those forces in the object’s material concreteness/contextual situatedness. Rather it acquires them from the procedures according to which it is, computationally, crafted. In order to be able to account for this perspective, we must consider in a non-metaphorical manner that Michael Hansmeyer works with structural grammars (most often subdivision processes). Hence, his designs acquire force in a similar manner as composed text acquires force: from being well-crafted in their abstractness. I will characterize such articulation as follows: (1) structural (transformational) grammars allow for articulating spatially what we can call ‚syntactical situations‘; (2) each joint in such an articulation is doubly-articulated, i.e. not determined by elements (within one axiomatics), but assessed by many processes of itemization and elementarization that contract symbolically whatever factors in in a common situation; (3) what counts as elements in such articulation is encrypted, and as such each one is, respectively, morphogenetic and parametric (it is not the building or the overall design which is parametric or morphogenetic); (4) the ‚purport‘ that is thereby being articulated and communicated, by deciphering and encryption, is, in principle, the entire corpus of architecture’s theoretical and sensible manifestations.

The crystallization of symbolic solids

We can follow a particular analogy to imagine the outlook of this view: as we can say that a structure doesn’t need a determinate form but can take many varying Gestalten (calculus-based form), so we can say that a crystal doesn’t embody a particular Gestalt, it solidifies universally and singularly (symbolic solids). Put differently, the object attains its manifest concreteness like a crystal concretizes, that is, through processes of phase-changes and solidification. A crystal’s relation between form and content is in no hylomorphic sense predetermined, and it is in no morphological sense determinable continuously and infinitesimally. The solidification process of a crystal accounts in discrete manner for whatever factors in and how it does so; like this, we can hold on to the distinction between form and content (as intelligible abstraction), expression and substance (as sensible/aisthetic manifestation), there is no need trying to conflate both by subjecting one to the other. Rather, we can think of both as contracted in a relation which Michel Serres characterizes as one of equipollence, meaning „sameness in force, effect, and significance“ (this kind of relation is central to his cosmical physics of communication, especially in The Parasite, and The Natural Contract).

Architecture’s inverse

I will read Hansmeyer’s recent work as explorations of what I suggest we could call, inspired by these considerations but especially also by Francois Laruelle’s mathematics-driven reconsideration of the philosophical notion of identity (in „Identity and Event“, Pli 9 (2000), 174-89), Non-Architecture, or Architecture’s Inverse. As such it is concerned with intra-architectural invariants, and the structures capable of conserving them throughout transformations.

Some lines of inquiry for discussion

– If the theoretical scope for architectures ought to include all it is and all it isn’t, of what ‚nature‘ is that scope then? Is it political? capitalist? cosmical? universal?

– What could be such infra-architectural ‚invariants‘?

– How can we understand this ‚force‘ an object acquires in such a materialism? The challenge being that if we render it as an aesthetic force, it would be an aesthetic of the intelligible as much as of the sensible.

– What happens to the notion of ‚aesthetic’ if we assume the peculiar character of a double-articulation (by taking an entire ‚scheme of partitioning‘ as ‚element‘ and ‚unit‘)

– How could we make sense of the processes of abstraction involved in a materialist informatics, how could we think of an architectural ‚subjectivity’?



The Building 1


The Building 2


The Building 3


The Building 4


The Building 5


The Building 6


The Building 7


The Building 8


The Building 9


The Building 10


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